Looks like they feed Purina. Like myself, feed Purina and have had zero issues with egg production. There's too many variables for egg production to label it one factor, especially "a feed conspiracy." Not everything has to be a conspiracy these days.
No, this still wouldn't prove anything. You'd have to do it like a scientific study, and do a control group. One "with" your normal feed, and the other group with the changed feed. This still wouldn't really prove anything though, because you'd need a lot of birds for good data.